Despite the existing evidence given by published meta-analyses, the cognitive profile of MD remains incomplete and not applicable in typical settings. Specifically, we identified three key issues which our meta-analysis addresses. First, DSM or ICD are mostly used to diagnose MD. However, no review so far has applied inclusion criteria similar to diagnostic criteria stated by DSM and ICD. Second, domain-specific abilities have never been systematically summarized yet although they are most important for MD identification. Instead, domain-general abilities were the focus of meta-analyses in the past. And third, it is unclear if strengths or weaknesses in abilities are similar if different scoring types are used (e.g., accuracy and response time). So far, meta-analyses focused mainly on accuracy scores and it is unclear, if response time scores can be used for MD identification.

We searched for studies which compared a group with MD with a typically developing group (TD) on any cognitive measure. The literature search was conducted in February 2021 using the following databases: PsycINFO, MEDLINE, ERIC, ProQuest, PSYNDEX and MathEduc. ProQuest and PSYCINFO were also used to find relevant dissertations and master’s theses. In addition, we searched the following published reviews about MD for relevant citations: Geary (2004, 2010, 2011), Swanson and Jerman (2006), Swanson et al. (2009), Johnson et al. (2010), Raghubar et al. (2010), David (2012), Peng and Fuchs (2014), Shin and Bryant (2015), Peng et al. (2016), Peng et al. (2018), and Vanbinst and de Smedt (2016).

Depending on the database, we searched with English and/or German search terms using title, abstract and keywords as search fields. To find studies comparing people with and without MD, we combined keywords for MD with keywords for difference and group membership using AND (see Supplementary Material).

Figure 1 provides a flow chart of the literature search according to Moher et al. (2009). The literature search initially provided 3039 studies. After removal of duplicates and application of every inclusion criteria, the number of studies was narrowed down to 35. The quality of those studies was assessed by using the Appraisal Tool For Cross-Sectional Studies (AXIS) (Downes et al., 2016), which confirmed proper study quality for all studies. Three studies were based on the same data set (de Weerdt et al., 2013a,b; Desoete and de Weerdt, 2013), which we therefore treated as a single study. One study (Schleifer and Landerl, 2011) consisted of three sub-studies with different samples, which we considered as 3 different studies. The remaining total pool of 34 studies was divided into 12 different data sets based on scoring and level of every outcome (see Section “Coding Procedures”). For every data set we applied risk of bias analysis and excluded outcomes with a very small number of studies (see Section “Statistical Methods”). Depending on the data set, 1–4 studies were excluded. For data set RT - TC (i.e., response time scores without time constraints) only 3 studies could be identified in total. After risk of bias analysis, no study remained, thus we could not perform any meta-analysis for data set RT - TC.

The MD and TD groups each had at least two persons. All included studies were published either in English or German. Because of the language skills of both authors, no other languages could be considered. Publication year of all studies was not before 1992 (publication year of ICD-10).

The MD was defined as a percentile rank at or below 16 in a standardized math test, a lag of at least 18 chronological or 15 instructional months in math (i.e., at least 1.5 years or 1.5 grades), or an existing diagnosis of MD (DSM- IV/5: 315.1; ICD-10: F81.2). Although other criteria and cut-offs exist to diagnose MD (Möller et al., 2012; Kaufmann et al., 2013), we chose PR ≤ 16 (i.e., one standard deviation) since it is recommended as cut-off in DSM-5.

All participants of our included studies received regular education (i.e., no special education) and were between 8 and 12 years old. In case years of age were not reported, participants had to attend 2nd to 6th grade. According to DSM and ICD, MD manifests during the first years of formal schooling and is mostly diagnosed during primary education (Nelson and Powell, 2018). Although very severe math difficulties can already be identified at a very young age (Stock et al., 2010), math performance of students in 1st grade still varies too much for MD identification (Kohn et al., 2013; Koponen et al., 2018). For this reason, we restricted the age range to the typical age range in which MD is usually identified.

For every study, MD and TD groups were matched for age or grade and for gender to control for age-moderated and gender-moderated differences between both groups, respectively.

To control for other causes for low math performance, only studies about MD were included in which, first, math performance was not primarily associated with a genetic or neurological disorder like fragile X syndrome (Murphy, 2009), Turner syndrome (Baker and Reiss, 2016), 22q11.2 deletion syndrome (de Smedt et al., 2009; Brankaer et al., 2016), neurofibromatosis type I (Orraca-Castillo et al., 2014), cerebral palsy (van Rooijen et al., 2015), epilepsy (van Iterson et al., 2015). Second, MD was not primarily associated with low birth weight or premature birth (Taylor et al., 2009; Jaekel and Wolke, 2014). And third, studies controlled for intellectual disability which was defined in accordance with DSM and ICD as an IQ lower than 70. Since an IQ of 70 is relatively low, studies reporting an “average IQ” as their selection criteria were included too.

Because 20–40% of people with MD also show low reading performance (Dirks et al., 2008; Landerl and Moll, 2010; Fischbach et al., 2013; Willcutt et al., 2013; Moll et al., 2014), we included only studies which controlled for reading difficulties (RD). Analogous to MD, RD was defined as a percentile rank above 16 in a standardized reading test, a lag of less than 18 chronological or 15 instructional months in reading (i.e., less than 1.5 years or 1.5 grades), or no existing diagnosis of RD (DSM-IV/5: 315.0; ICD-10: F81.0; ICD-11: 6A03.1).

As a final inclusion criterion, all studies had to report enough data to compute effect sizes based on the standardized mean difference between both groups.

For the descriptive variables, we coded study, sample, and diagnostic characteristics. Study characteristics included (a) year of publication and (b) type of publication. Sample characteristics of MD and TD group were (a) sample size, (b) mean age in months, and (c) percentage of male participants. Diagnostic characteristics contained (a) measures of IQ, reading and math performance; (b) criteria used to exclude intellectual disabilities and RD, and criteria used to diagnose MD; and (c) if ADHD was excluded or not.

For the outcome variables, we used an exploratory approach according to Brown et al. (2003). That meant instead of defining a coding scheme for study outcomes in advance we derived relevant coding categories for the outcomes from the included studies themselves. This approach reduced the risk of excluding important data a priori by not-coding relevant outcomes and was therefore most suitable to derive a comprehensive cognitive profile of MD. Furthermore, precision of effect size estimations increased since we could consider dependent correlations between outcomes which could have otherwise been ignored (Riley, 2009).

We started this exploratory coding approach by separating between the scoring and level of every outcome of every study. For scoring, we coded for each outcome if accuracy (AC; e.g., number of solved items) or response time (RT; e.g., mean response time for solved items) was measured and if any time constraints were involved (TC; e.g., time limit, instructed to “work as quickly as possible”). This resulted in 4 different categories for scoring: Accuracy without time constraints (AC − TC) and with time constraints (AC + TC) as well as response time without time constraints (RC − TC) and with time constraints (RT + TC).

For level, we coded every outcome on the following three hierarchical levels of abilities in accordance to their description in the Introduction: High-level ability (HA), medium-level ability (MA), and low-level ability (LA). First, we assigned study outcomes to the same low-level abilities when they shared a similar operationalization (e.g., counting forward from 1 to 10 and counting backward from 8 to 2 was defined as low-level ability number word knowledge). Second, we assigned similar low-level abilities to its respective medium-level abilities (e.g., low-level abilities number word knowledge and quantity processing were assigned to medium-level ability number sense). Third, we assigned medium-level abilities to its corresponding high-level abilities (e.g., medium-level abilities number sense and computing were assigned to high-level ability mathematics). For better understanding, high-level, medium-level and low-level ability can also be referred to as first-order, second-order and third-order factor, respectively. If we could not assign a study outcome to a single low-level ability (e.g., index scores which comprised several low-level abilities) this outcome was only assigned to its respective medium-level or high-level ability (e.g., a single outcome comprising tasks measuring quantity processing and numerical relations was only assigned to medium-level ability number sense and high-level ability mathematics). Taken together, a single outcome was coded on one of four different categories for scoring (AC − TC, RT − TC, AC + TC, and RT + TC) and on three different levels (HA, MA, and LA) which resulted in 4 × 3 independent data sets of coded outcomes. See Supplementary Table 1 for the final coding scheme.

Based upon the set of included studies the first author and a student assistant developed the coding scheme by scanning all reported study outcomes as described above. In case of disagreements, the relevant study outcomes were discussed until a consensus was reached. After the coding scheme was finalized, all descriptive and outcome variables were coded. The first 10 studies were double-coded by the first author and the student assistant. Inter-rater agreement varied between 88 and 97% using Cohen’s kappa (Cohen, 1960) for nominal and intraclass correlation coefficients (Hallgren, 2012) for ordinal or higher levels of measurement, respectively. Lower agreement rates were due to incomplete descriptions of diagnostic cut-off criteria, tests, and measures provided by the studies.

In case of missing data, we contacted the study’s authors. If they didn’t provide the data, effect sizes and standard deviations were computed by transforming reported data using formulas provided by Borenstein (2009). If transforming was not possible, we differentiated between descriptive and outcome data. In case of missing descriptive data, studies were excluded from further analysis if the missing data was related to the inclusion criteria of the meta-analysis. This was done to ensure a clean data set strictly according to our criteria. For missing outcome data, studies were excluded if there was a high risk of a selective outcome reporting bias (Pigott et al., 2013) according to AXIS. Serious selective outcome reporting indicated that a study was strongly biased toward certain conclusions. This also made it unclear, if the methods (esp. statistical procedures) were properly conducted and if we could trust the outcomes which were reported. For this reason, we excluded those studies instead of trying to address this issue by using risk of bias analysis. However, no study had to be excluded because of serious selective outcome reporting.

We assessed the quality of each study by using the Appraisal Tool For Cross-Sectional Studies (AXIS) (Downes et al., 2016) which contains 20 yes/no questions evaluating the quality of reporting, study design, and possibility of bias of cross-sectional studies (e.g., “Was the target population clearly defined?”, Were the limitations of the study discussed?”). The final judgment about study quality is determined by an overall subjective assessment of every item since no numerical rating scale is provided.

Initially we coded 9 high-level abilities, 19 medium-level abilities and 13 low-level abilities. After we separated the overall data set into the corresponding data sets for accuracy and response time with or without time constraints and after we excluded outcomes with a very small number of studies only 5 high-level abilities, 9 medium-level abilities and 8 low-level abilities remained which were included in the meta-analysis. For domain-specific abilities most outcomes fulfilled our criterion and were reported by at least 3 studies with at least 2 different first authors (see Section “Statistical Methods”). However, for domain-general abilities we had to exclude most of the coded outcomes. We did not find more than 2 studies for high-level abilities processing speed, visual processing, learning efficiency, and comprehension knowledge. As a result, our analysis about domain-general abilities only covered short-term working memory (16 studies), reaction and decision speed (3 studies) and fluid reasoning (3 studies).

All analyses were conducted using R (R Core Team, 2020) and R package robumeta (Fisher et al., 2017). We used the standardized mean difference between the MD and TD group as effect size measure. For this reason Hedges’ g (Hedges, 1981) was calculated which corrects Cohen’s d (Cohen, 1969) for a small sample bias.

Before conducting the meta-analysis, we applied several measures to reduce the risk of bias in individual studies (e.g., selective reporting) and across studies (e.g., publication bias). Studies were excluded if AXIS indicated a low study quality and a high risk of reporting bias. To reduce the influence of outliers within each data set we applied a 90% Winsorizing to these effect sizes (Dixon, 1960). That is, effect sizes below the 5th or above the 95th percentile were set to the 5th or 95th percentile, respectively.

Outcomes were excluded, if they were not reported by at least 3 studies which in addition were published by at least 2 different first authors. The validity of a meta-analysis depends more on the expected heterogeneity and quality of the studies included than the total number of included studies (Valentine et al., 2010). Since our study sample was well defined because of stringent inclusion criteria (e.g., small age range and clinical diagnostic criteria) and since each study was critically appraised by using a checklist, we expected rather similar effect sizes and smaller standard errors for outcomes. For this reason, we accepted a smaller number of studies per outcome as sufficient. We specifically settled on 3 studies as the minimum number of studies per outcome in the unlikely event that the effect sizes of 2 studies were very contrasting so that the effect size of the third study could give us the right direction of the overall average effect size. The additional criterion of at least 2 different first authors for each outcome was necessary to reduce the risk of authorship bias (Moulin and Amaral, 2020) since the number of researchers focusing on MD is small.

Regarding the analysis, most studies provided more than one outcome and multiple effect sizes for each outcome. To account for statistical dependencies of multiple outcomes and effect sizes from the same studies (Jackson et al., 2011; Moeyaert et al., 2017) we performed a robust variance estimation method based on a random effects model (RVE; Raudenbush, 2009; Hedges et al., 2010; Tipton, 2015). Although we used strict inclusion criteria, we applied a random effects model because we still expected effects of the same outcomes to vary across studies. The RVE method corrects the standard error of the average effect size estimate by taking into account the correlations between effect sizes from the same sample (i.e., same study). For this, an estimation of the mean correlation between all pairs of effect sizes within a study is needed. We chose p = 0.70 which is a rather conservative estimate to reduce the risk of a type I error. In addition, we performed sensitivity analysis with various estimates of p to examine the robustness of our results. But, as Hedges et al. (2010) already pointed out, the estimate of the mean correlation has actually no considerable effect on the standard error estimates.

After the analysis, we conducted several meta-regressions to assess risk of bias across studies. For every outcome we applied the same criterion regarding minimum number of studies as for the overall analysis. That is, a meta-regression was only performed if the respective moderator was reported by at least 3 studies which were published by at least 2 different first authors. To examine publication bias, we applied Egger’s regression test (Egger et al., 1997) and Funnel plot tests (Sterne and Egger, 2001) which examine the influence of the standard errors and the sample size on the estimated average effect sizes, respectively. Both tests, when significant, indicate the presence of a small-study effect which means that too many studies with small sample sizes and large effect sizes are in the data set. However, it should be noted that both tests are prone to false positive results, especially when heterogeneity in the data is high (Rodgers and Pustejovsky, 2020). We created no funnel or forest plots since both type of plots did not account for statistically dependent effect sizes thus making any interpretation misleading (Doleman et al., 2020). To control for biases based on the characteristics of the TD and MD group (e.g., selection bias) we analyzed the moderating effect of severity of MD (i.e., difference in math performance between groups) as well as differences in IQ and reading performance between groups.

In total and across all data sets 34 studies were included, comprising 320 effect sizes. The total MD sample consisted of 680 unique people (43.6% male) with a mean age of 117.3 months and the total TD sample covered 1565 unique people (48.4% male) with a mean age of 117.5 months. Regarding IQ, 85.3% of all studies measured non-verbal IQ or a combination of non-verbal and verbal IQ. Cut-off used to exclude low IQ ranged from 80 to 90. Regarding reading performance, 88% of all studies measured reading fluency or a combination of reading fluency and reading comprehension. Most studies (85.3%) applied percentile ranks to exclude RD, which ranged from percentile rank 16 (the pre-defined minimum) to 40. Only 5.9% or 8.8% of all studies used delays in months or an existing diagnosis of RD as exclusion criteria, respectively. Regarding math performance, 97.1% of all studies measured computation or a combination of computation with number sense and/or math reasoning. Similar to reading performance, most studies applied percentile ranks to define MD, which ranged from percentile rank 5–16 (the pre-defined maximum). For MD, 20.6% or 8.8% of all studies used delays in months or an existing diagnosis of MD as inclusion criteria, respectively. Regarding ADHD, less than half of all included studies (47.1%) controlled for ADHD within their samples. Descriptive information and assignment of studies to each data set are listed in Table 1.

The size of the effect is interpreted according to Cohen (1988) (i.e., none or not relevant: g < 0.2; small: 0.2 ≤ g < 0.5; medium: 0.5 ≤ g < 0.8; large: g ≥ 0.8). In addition, only medium to large effect sizes were considered as a particular strength or weakness. Positive effect sizes reflect better scores in favor of the TD group (e.g., higher accuracy and faster response time) and vice versa. We had to control for type I error when determining statistical significance since degrees of freedom were small for some abilities. In line with Tanner-Smith et al. (2016), p < 0.05 was used when degrees of freedom were greater than or equal 4 and p < 0.01 when degrees of freedom were less than 4.

Table 2 lists the estimated effects for high-level abilities, medium-level abilities, and low-level abilities for data sets AC − TC and AC + TC, and RT + RT. To facilitate comparison of scoring and level of outcomes, not all statistics have been reported in Table 2 (e.g., confidence intervals). An extensive list of all statistics is provided by Supplementary Table 2. For a better overview of the results, the estimated effects are shown in Figure 2.

All included outcomes were in favor of the TD group. However, for medium-level abilities and low-level abilities the number of studies was small and p < 0.01 was mostly used as significance level. As a consequence, most outcomes were not statistically significant.

Regarding domain-specific abilities, the MD group showed significant weaknesses in high-level ability mathematics regardless of data set. However, weaknesses in accuracy without any time constraints were usually large compared to medium weaknesses in accuracy with time constraints or response time with time constraints. Especially low-level ability calculation and medium-level ability math reasoning were more affected in people with MD compared to low-level ability fact retrieval. For medium-level ability number sense, results were mixed and dependent on the data set. Effect sizes for low-level ability numerical relations (i.e., mostly symbolic comparison tasks) were large in all data sets, but only significant in data set AC - TC. This was interesting compared to low-level ability quantity processing (i.e., mostly non-symbolic comparison tasks). Here, effect sizes were medium and significant in data set AC + TC while only a small and non-significant effect size could be found for data set RT + TC. Also, low-level ability quantity-number linking (e.g., subitizing and dot enumeration) was larger and significant for data set RT + TC compared to data set AC + TC. Low-level ability number word knowledge (e.g., counting) was only reported for data set AC − TC and a large effect size was found.

For high-level ability reading and writing and their corresponding medium and low-level abilities effect sizes were either small or not-relevant and not-significant. Also, for low-level ability naming facility, which included RAN tasks with numbers as stimuli, we did not find a weakness for people with MD. However, small effect sizes for reading and writing were to be expected since we controlled for RD in our sample of studies.

Regarding domain-general abilities, only some effect sizes for high-level ability short-term working memory were significant. In particular, effect sizes for medium-level abilities visual-spatial short-term storage and working memory were medium compared to small effect sizes for medium-level ability auditory short-term storage. We could not find significant effects for medium-level ability attentional control. The only difference was that effect sizes for data set RT + TC were larger compared to data set AC + TC. However, this was moderated more by the tasks than by MD status since tasks measuring attentional control (e.g., stroop task and flanker task) are usually designed around response time differences.

For high-level ability reaction and decision speed, people with MD showed no significant differences compared to people without MD. Also, no significant difference was found for high-level ability fluid reasoning which was also because all studies controlled for low IQ within their samples.

Results of risk of bias analysis are shown in Supplementary Table 3. For some outcomes the number of studies was too small to perform moderator analysis. To determine statistical significance, we used the same procedure as described above (i.e., p < 0.01 for df < 4; p < 0.05 for df ≥ 4). We only identified publication bias when outcomes were measured using time constraints (AC + TC and RT + TC). Egger’s test indicated a publication bias in data set AC + TC and in data set RT + TC for high-level ability mathematics and medium-level ability number sense, respectively. Otherwise, no other moderating effect for any ability could be identified. That is, sample size (i.e., funnel plot test), differences in IQ or reading performance and severity of MD did not significantly moderate the estimated effects in any data set.

Regarding domain-specific abilities, this was the first meta-analysis to even summarize abilities in this area. As expected, MD affects all mathematical abilities which is in line with previous research defining MD as a heterogeneous disorder (Kaufmann et al., 2013; Karagiannakis et al., 2014).

Our lack of results regarding domain-general abilities was surprising regarding the huge body of research published in recent years about the important role of domain-general abilities for math development (Taub et al., 2008; Henik et al., 2011; Fias et al., 2013). This is because we could not consider a lot of studies since they did not meet our inclusion criteria. Since we excluded RD, we did not find substantial weaknesses in those domain-general abilities typically associated with reading difficulties and comorbid math and reading difficulties: Auditory short-term storage, retrieval fluency and phonetic coding (Peng et al., 2017; Moll et al., 2019). Also, differences in reading performance between the MD and TD group did not significantly moderate effect sizes in any of the included abilities. While this cannot be considered as a particular strength compared to people without MD, it is important to point out that people with MD perform about as well as people without MD on these domain-general abilities. As a consequence, our results contradict those of other reviews which reported medium to large weaknesses and did not exclude RD or failed to mention the exact criteria (Swanson and Jerman, 2006; Swanson et al., 2009; Johnson et al., 2010; Peng et al., 2018). Those reviews also applied liberal criteria regarding cut-offs for MD or age range, so we are not able to pinpoint the exact reason for the different results. For phonetic coding we can provide an alternative explanation for the small effect size we found in our study. This ability is associated with the development of number word knowledge and knowledge about basic arithmetic facts (de Smedt and Boets, 2010; Pollack and Ashby, 2018). Only later are facts retrieved directly from memory and people rely less on phonetic coding. Like quantity processing an age-bias is possible, as our sample of participants could have been too old to have a more severe weakness in phonetic coding. Also, Moll et al. (2019) give hints as to why we even found effects, albeit very small ones, even though RD was excluded in our study. That is, domain-specific ability computation relies stronger on language abilities than number sense and is therefore stronger associated with reading abilities. Especially, retrieving arithmetic facts from memory depends more on the processing of verbal information compared to symbolic or non-symbolic magnitude comparisons. As a result, comorbidity rates between MD and RD are four times higher when MD identification is solely based on computation than on number sense. In our meta-analysis, 97.1% of all included studies applied computation tasks to identify MD. Although we excluded severe reading difficulties, we cannot rule out the possibility that our sample of people with MD still had minor problems in reading because of the tests used to identify MD. That being said, our findings are still in line with multiple studies comparing weaknesses in MD, RD, and MD + RD on these domain-general abilities (Schuchardt et al., 2008; Willburger et al., 2008; Cirino et al., 2015; Moll et al., 2015).

First, the number of studies for each outcome varied considerably and dropped with increasing specificity of outcomes (e.g., from high-level to low-level ability). While meta-analyses can be performed with no more than 2 studies, results are usually more robust and less prone to publication bias when more studies are included (Lin, 2018). Especially when random effects and a certain degree of heterogeneity between and within studies are expected, effect sizes based on the data of few studies need to be interpreted cautiously (Valentine et al., 2010). To solve this problem, we applied meta-regressions to examine the influence of moderating variables. However, also those measures are accompanied with various issues (e.g., low power for small sample size, no random assignment of studies to moderators) and therefore only give hints on possible data problems (Oxman and Guyatt, 1992; Walker et al., 2008; Wood and Eagly, 2009). Most importantly, we have therefore used strict inclusion criteria in accordance with DSM and ICD to derive valid results. On the one hand, those criteria were responsible for our small sample of studies. On the other hand, they led to a representative sample of MD without other corrupting conditions (comorbidities) or issues (broad age range and high cut-off value) usually accompanied with more liberal criteria. Nevertheless, Egger’s test also indicated a publication bias in data set AC + TC and in data set RT + TC for high-level ability mathematics and medium-level ability number sense, respectively. Although this does not fundamentally contradict our findings, a small-study effect for those abilities is possible.

Second, across all data sets, heterogeneity I² (Higgins and Thompson, 2002) was substantial and on average 57.5% (AC − TC: 53.6%, AC + TC: 52.6%, RT + TC: 66.4%). Although descriptive information of all included studies indicated a homogenous data set, there is inconsistency in the data which was neither accounted for by our statistical model nor further explained by any moderator we applied. Also, heterogeneity was larger for response time scores than for accuracy scores. From a methodological perspective, small samples tend to increase heterogeneity (IntHout et al., 2015). Also type of scoring could have affected heterogeneity. Data set RT + TC had the highest heterogeneity, the smallest sample size and studies varied considerably in how they measured response time scores (e.g., total time and time for correct answers), detected outliers, or transformed data (e.g., log transformation). Those variations may have affected effect sizes, hence led to greater inconsistencies between studies in data set RT + TC. From a theoretical perspective, Kaufmann et al. (2013) defined heterogeneity as a feature of MD. According to them, people with MD have a core weakness in domain-specific abilities which can be accompanied by weaknesses in domain-general abilities as well. However, the type and severity of all those weaknesses varies depending on the neurofunctional and behavioral development of each individual person with MD. As a result, differences between people with and without MD are less moderated by study design. Instead, heterogeneous manifestations of MD exist within every MD sample due to interindividual neurodevelopmental differences (Zhang et al., 2017; McCaskey et al., 2018). This perspective is also in accordance with a vast research body about different subtypes of MD (Landerl et al., 2004, 2009; Gold et al., 2013; Bartelet et al., 2014; Cirino et al., 2015; Shin and Bryant, 2015; Träff et al., 2017). However, such research questions can only be answered by using controlled studies. While we do not deny the possibility of different subtypes of MD to explain the overall heterogeneity, we can neither test nor control for it. The scope of this meta-analysis was to summarize strengths and weaknesses of MD based on clinical criteria.

Third, ADHD was not deliberately excluded by us. About 10–20% of people with MD also have ADHD or show symptoms thereof (Gross-Tsur et al., 1996; Fortes et al., 2016). Kuhn et al. (2016) have shown that the profile of people with MD + ADHD is a combination of the distinct weaknesses of people with MD or ADHD. Only 16 out of 34 studies of our sample controlled for ADHD. And those who did relied mostly on existing information instead of applying any additional measures. As a result, studies including comorbid cases of MD + ADHD are possible and effect sizes for ADHD-specific outcomes like attentional control were interpreted carefully.

Fourth, studies that did not control for reading difficulties were excluded rather than being coded and used as moderator. We refrained from using a subgroup analysis to compare effect sizes of studies that excluded RD to those that did not for two reasons. First, for studies that did not exclude RD we could not make any assumptions about the distribution of reading performance within each sample. Especially if reading performance was not measured people with RD could have been in the sample thus co-founding the subgroup analysis. Second, subgroup analyses have been criticized for their low statistical power because categories with a different amount of studies and varying study quality are being compared (Oxman and Guyatt, 1992; Walker et al., 2008). While meta-analyses are based on a systematic literature following clear inclusion criteria, subgroup analyses are only observational (i.e., cross-sectional studies) because neither are the studies randomly assigned to each group nor are any moderating variables being controlled for (Higgins and Green, 2011). While this problem also applies to meta-regressions, it is especially pronounced for subgroup analyses. Since this meta-analysis had already to deal with low sample sizes because of our conservative inclusion criteria, we decided that the statistical power of any subgroup analysis would have been too low to allow any conclusions. This also applies to ADHD for which we did not perform a subgroup analysis either.

Fifth, we did not find any particular strength for the MD group based on the effect size. There were many small effect sizes which we refrained from classifying as a particular “strength” or “non-weakness.” By using the terms “strength” and “weakness” we tried to emphasize our exploratory coding approach. Since we did not restrict our coding scheme to certain abilities, we could not rule out that a medium to large effects sizes in favor of the MD group in any ability was theoretically possible.

We identified a cognitive profile of domain-specific and domain-general deficits of MD which is based on criteria according to the DSM and ICD. Whereas DSM and ICD only describe in a very general way which abilities are affected in MD, we found a distinct set of well operationalized abilities which evidently differ best between groups of children (8–12 years old) with and without MD. These were: Calculation (AC − TC), fact retrieval (AC + TC), quantity processing (AC + TC), quantity-number linking (RT + TC), numerical relations (AC − TC), and visual-spatial short-term storage (AC − TC). This profile helps experts working with DSM or ICD to revise their general diagnostic procedures und treatment plans. Also, for clinical guidelines about diagnostic and treatment of MD, our profile serves as high quality evidence-based information derived by a systematic literature and meta-analysis. However, we also want to point out that this profile is based on average group differences and therefore cannot account for the heterogenous development of MD in individuals.

Our meta-analysis was the first in many aspects. We used stringent inclusion criteria according to DSM and ICD, summarized domain-specific abilities in a systematic way, applied a multi-level coding scheme and differentiated scoring types. While this approach was very laborious and needed many adjustments, it resulted in a comprehensive profile about MD which has various implications for further research. Most importantly, when controlling for reading difficulties MD is not accompanied by substantial weaknesses in those domain-general abilities which are typically assigned to reading (i.e., phonetic coding, naming facility, and auditory short-term storage). Also, visual-spatial short-term storage is more affected in MD compared to auditory short-term storage which emphasizes the notion that number and space are interlinked and overall important for math development. In the past, multiple fMRI studies have reported neuronal activity in areas allocated to domain-general abilities when doing arithmetic and even suggested a neuronal network of domain-specific and domain-general abilities (Kucian, 2016; Peters and de Smedt, 2018). If and how this applies to MD is still unknown. Unfortunately, also our meta-analysis could not derive a distinct pattern of strengths and weaknesses in domain-general abilities since most studies about domain-general abilities did not meet our stringent inclusion criteria. A pressing need for high quality studies investigating those abilities is obvious.